Matrix superpotentials and superintegrable systems for arbitrary spin

TL;DR

This paper explicitly solves a set of quantum superintegrable systems with arbitrary spin using supersymmetric quantum mechanics, revealing their matrix shape invariant potentials and expanding understanding of superintegrability.

Contribution

It introduces a new explicit solution method for superintegrable systems with arbitrary spin, connecting to recent classifications of matrix shape invariant potentials.

Findings

Explicit solutions for superintegrable systems with arbitrary spin

Identification of matrix shape invariant potentials

Extension of supersymmetric quantum mechanics techniques

Abstract

A countable set of quantum superintegrable systems for arbitrary spin is solved explicitly using tools of supersymmetric quantum mechanics. It is shown that these systems (introduced by Pronko, J. Phys. A: Math. Theor. 40 (2007) ) include matrix shape invariant potentials classified recently in A. G. Nikitin and Y. Karadzhov, J. Phys. A: 44 (2011) 305204; J. Phys. A: 44 (2011) 445202.